Postgres 9.5

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create table domain_lifecycle (
domain varchar,
timestamp timestamp,
lifecycle varchar);
insert into domain_lifecycle values
('example_1.com', '2020-01-01 01:01:00', 'start'),
('example_1.com', '2020-01-01 01:01:05', 'end'),
('example_2.com', '2020-01-01 01:01:07', 'start'),
('example_2.com', '2020-01-01 01:01:17', 'end'),
('example_3.com', '2020-01-01 01:01:20', 'start'),
('example_1.com', '2020-01-01 01:01:25', 'start'),
('example_3.com', '2020-01-01 01:01:23', 'end'),
('example_1.com', '2020-01-01 01:01:38', 'end');
8 rows affected

SELECT DISTINCT
       domain
       FROM domain_lifecycle c1
            CROSS JOIN LATERAL (SELECT min(timestamp) "timestamp"
                                       FROM domain_lifecycle c2
                                       WHERE c2.domain = c1.domain
                                             AND c2.lifecycle = 'end'
                                             AND c2.timestamp >= c1.timestamp) c3
       WHERE c1.lifecycle = 'start'
             AND c3.timestamp - c1.timestamp >= '5 seconds'::interval;


domain


example_1.com

example_2.com